Related Subreddits:

Allowed

A discussion where you ask a question of the global community so that you can expand your view on a topic, incite conversation or collect and verify specific data. Discussions should respect the opinion of all who participate.

Instructional resources

News and article reviews

Blog post reviews

Disallowed

Memes, funny screenshots, comics

Editorialized/sensationalized titles

Giveaways, trading, begging

Petitions, surveys

Blog post copypasta

Sales pitches

Job postings

Webinar invitations

Network marketing or MLM (Multi-Level Marketing)

Religious, political or non-profit discussions except in that they relate to social media aspects

I'm trying to sell social media to several clients. I'd like to leverage stats to show them how beneficial it can be for individual industries. I already have basic stats like number of users on each platform but I want to go more in depth. (ex. Growing demographics)

Are there any sites that sell or give away reports similar to Nielsons but for Social Media?

You don't grow demographics. You grow communities, audiences, fan-bases, etc. Just to be clear.

I would recommend finding some best-in-class use cases for how brands and businesses in the industries you're looking at have used social media to meet specific objectives. There are often publishes in articles, blogs, and as case studies and will usually include the results (since it's being heralded as a successful campaign).

That's the most basic approach I'd recommend, as long as you're not claiming credit for the examples and just using them to show potential benefits of social media.